Quantifying Charge Carrier Recombination Losses in MAPbI3/C60 and MAPbI3/Spiro-OMeTAD with and without Bias Illumination

To increase the open-circuit voltage in perovskite-based solar cells, recombination processes at the interface with transport layers (TLs) should be identified and reduced. We investigated the charge carrier dynamics in bilayers of methylammonium lead iodide (MAPbI3) with C60 or Spiro-OMeTAD using time-resolved microwave conductance (TRMC) measurements with and without bias illumination (BI). By modeling the results, we quantified recombination losses in bare MAPbI3 and extraction into the TLs. Only under BI did we find that the density of deep traps increases in bare MAPbI3, substantially enhancing trap-mediated losses. This reversible process is prevented in a bilayer with C60 but not with Spiro-OMeTAD. While under BI extraction rates reduce significantly in both bilayers, only in MAPbI3/Spiro-OMeTAD does interfacial recombination also increases, substantially reducing the quasi Fermi level splitting. This work demonstrates the impact of BI on charge dynamics and shows that adjusting the Fermi level of TLs is imperative to reduce interfacial recombination losses.


Sample Preparation
215 nm thick MAPbI 3 thin films have been prepared by spin-coating a 37 wt% solution of MAI (synthetized following standard procedure 1 ) and Pb(Ac) 2  3H 2 O (Sigma-Aldrich) powders (3:1 ratio) in DMF. The solution was spin-coated on plasma cleaned quartz plates at 2000 rpm for 45 s in a nitrogen filled glovebox and left to dry for 15 minutes at room temperature. The films have been annealed at 100C for 5 minutes.
Selective transport materials have been deposited on top of the MAPbI 3 films via the following procedures: 30 nm C60 layer has been thermally evaporated, while a 75 mg/mL solution of Spiro-OMeTAD in chlorobenzene has been spin-coated at 1500 rpm for 45 s. The samples been then dried for 1 hour at 60C to remove the remaining solvent.
The XRD spectrum of the MAPbI 3 thin film is shown in Figure S1. XRD measurements have been performed with a Brüker D8 diffractometer (Co Kalfa-1, 1.78Å) Figure S1: MAPbI 3 thin film XRD spectrum.

Bias Illumination
To determine the generation profile, G Bias , for fitting the TRMC measurements recorded with bias illumination, the following procedure was used as also described by Guo et al. 2 First the light intensity of the white light LED (see emission spectrum in Figure S2a) at the sample position has been measured with a Silicon photodiode (Coherent, OP-2/LM-2 VIS) yielding a value of 13.5 mWatt cm -2 . This intensity matches to the total number of integrated photons of the white light LED. Next, we integrated the number of photons over the wavelength emission range of the LED, however now corrected for the fraction of absorbed photons yielding values for G Bias of 6.74, 6.79 and 6.46×10 20 cm -3 s -1 in the pristine MAPbI 3 , MAPbI 3 /C60 and MAPbI 3 /Spiro-OMeTAD, respectively. The absorbance spectra are shown in Figure S2b.
To relate the observed values of G Bias to AM1.5 we corrected the LED spectrum for the solar emission spectrum and the absorbance spectrum of the photoactive layer (shown in Figure S2c). After integration this corrected emission spectrum over the wavelength, the G Bias profile corresponding to AM1.5 is found. Figure S2: a) LED emission profile; b) fraction of absorbed (solid lines), F A , and reflected (dashed lines), F R , of pristine MAPbI 3 (red), MAPbI 3 /C60 (green), and MAPbI 3 /Spiro-OMeTAD (orange) films; c) AM1.5 spectra not corrected (black), corrected for LED emission profile (blue), and F A of the MAPbI 3 sample used in this study.

Microwave Conductance Technique
A schematic representation of the microwave conductance set-up is shown in Figure S3. While an accurate description of its working principles can be found elsewhere, 3 it is of relevance to underlying fundamental distinctions during the different operation modes applied in this study. Steady-state microwave conductance (SSMC) measurements have been conducted in the dark and in presence of bias illumination only. In the former case, it is possible to extract information regarding the background conductivity of the system under investigation. This is done by performing a scan of the microwave power over a broad frequency range (8.2-12.2 GHz) in a resonant cavity, and analyzing the dip of microwave power at the resonance frequency. In fact, the deep observable at the resonance frequency is not only related to the cavity's properties, but also to the dimensions, dielectric properties and conductivity of the sample analyzed. In a previous study we have demonstrated how it is possible to extract the conductivity, , by fitting the resonance dip. 4 Furthermore, steady-state concentration of photogenerated charge carriers can be calculated from the conductivity measurements during steady-state illumination, as it was done in the study presented by Guo et al. 5 In this paper, we have performed SSMC measurements in the dark, see Figure S4, and in presence of bias illumination, as shown in Figure 4d in the main text. From Figure S4 it is possible to notice a higher microwave power detected at the resonance frequency for MAPbI 3 /Spiro-OMeTAD compared to pristine MAPbI 3 . As discussed in the main text, this is an indication of reduced background conductivity in the bilayer. On the other hand, from the fittings of the SSMC results under bias illumination we have estimated the conductivity of the MAPbI 3 layer, and estimated the number of charge carriers, n, in the material according to: (Eq. S1) = ∑ where e is the elementary charge and  the sum of electron and hole mobilities. From this analysis it is not possible to directly discriminate the electron and hole contributions. Nonetheless, we can use the estimated values to validate the TRMC model, as described in the main text. The homogeneity of excitation throughout the sample has been tested by performing the same experiments upon FS illumination, i.e. from the perovskite and TM side. The results are shown in Figure S5. The lower magnitude of MAPbI 3 /C60 sample in Figure 5b compared to the single layer can be explained by the increased fraction of absorbed bias light in the TM layer, which is now directly irradiated.

Modelling TRMC measurements
Similar to equations 2-5 in the main text, the differential equations used to fit the TRMC traces of the MAPbI 3 /Spiro-OMeTAD heterojunction are: To come to the photoconductance the excess electrons and holes are multiplied by their mobilities according to

Global, iterative fitting procedure
In absence of bias illumination (only pulsed excitation, G P ): 1. N T , k T and k D , and charge carrier mobilities in the bare MAPbI 3 layer are obtained by fitting TRMC traces recorded with intensities yielding n <= N T . (see also reference 3.
2. Next, k 2 is obtained by fitting TRMC traces over a wider intensity range. Quality of fits is assesed in lin/lin as well as log/lin representation.
3. For the bilayers, the parameters found in steps 1 and 2 are kept constant, while values for and are increased until a good match is found for traces recorded at different intensities.
In presence of bias illumination (G com ): 4. The bare MAPbI 3 traces are fitted with the values obtained from steps 1-2.
5. Small changes are introduced on the parameters which are most likely affected by the BI, e.g. N T in MAPbI 3 .
6. Similarly to step 5, fits to the bilayers' traces are performed keeping most variables constant untill decent match is found with one set of parameters.